Coefficient Estimates for Analytic and Bi-Univalent Functions Classes Defined by Generalized Mathieu-Type Power Series

In this paper, we introduce two novel subclasses, MSκ*(δ,β,μ) and NSκ*(φ), of analytic and bi-univalent functions associated with generalized Mathieu-type power series in the open unit disk. By employing coefficient-based techniques, we derive new bounds for the initial Taylor–Maclaurin coefficients and the Fekete–Szegö functional for functions belonging to these subclasses. The obtained results contribute to the ongoing development of coefficient problems in geometric function theory and provide a unified framework that extends several known results in the literature. Additionally, we present a range of special cases that recover previously studied function classes, thereby highlighting the flexibility and applicability of the proposed approach.